CAIRO, Egypt (CNN) -- Egypt's top prosecutor opened an investigation Thursday into claims that Mohamed Morsy and top leaders of the Muslim Brotherhood incited violence and the killing of protesters, a day after the military ousted the country's first democratically elected president.
The prosecutor, Gen. Abdel Maquid Mahmoud, issued an order preventing Morsy and 35 others from leaving the country while they are under investigation, state-run Middle East News Agency and EgyNews reported.
The news came as Egypt's security forces moved to arrest leaders of the Muslim Brotherhood who supported Morsy's rule and to silence their communications outlets.
Muslim Brotherhood spokesman Gehad El-Haddad told CNN that Morsy was initially under house arrest at the presidential Republican Guard headquarters in Cairo and later moved to the Ministry of Defense; the military has not commented on Morsy's whereabouts.
The news from MENA and EgyNews appear to contradict reports that Morsy refused an offer by the armed forces to leave Egypt for Qatar, Turkey or Yemen. The state-run newspaper Al-Ahram reported Thursday Morsy would not step down voluntarily and that his speech Wednesday -- shortly before his ouster -- represented a "flagrant challenge to (the military's) authority" and a "declaration of confrontation with it."
A spokesman for Morsy's Freedom and Justice Party said that what started as a military coup was "turning into something much more."
In an interview in Cairo, El-Haddad cited the arrests as "very, very questionable attempts by the military to dismantle the Brotherhood."
He added, "This is a military coup that's establishing an oppressive new regime under the whitewashed face of the old regime."
The military should not take political sides, he said. Though he had had no direct communications with Morsy, sympathizers within the military were giving information to the Brotherhood, he said.
The former chairman of the Muslim Brotherhood, Mahdi Aakef, and his bodyguards were arrested Thursday in Cairo with four weapons in their possession, according to MENA, which cited security sources.
And Muslim Brotherhood supreme leader Mohamed Badei and the former supreme leader Mohamed Mahdi Akef have been arrested, Egyptian state broadcaster Nile TV said Thursday.
Badei was arrested for "incitement to murder," according to the arrest report cited by Al-Ahram. Police are seeking another 300 members of the Muslim Brotherhood, Al-Ahram reported.
On Wednesday, police closed the studios of pro-Muslim Brotherhood television stations Misr 25, The People and al-Hafez and arrested some of the journalists, according to Al-Ahram.
Despite the moves against the Brotherhood, the military suggested Thursday it would protect the movement's members. It said it would not allow any attacks or intimidation against those who belong to an Islamic group, state-run Nile TV reported. Even so, sporadic violence at times pitted Morsy's supporters against the opposition and the military, raising fears of spiraling unrest.
Clashes were reported at a pro-Morsy rally Thursday in the northern city of Zagazig, Nile TV reported, citing security officials. Thirty-two people were killed Wednesday in clashes in Egypt, officials told Nile TV. Hundreds more were reported to have been injured.
On its website, the Muslim Brotherhood declared "our unequivocal rejection of the military coup against the elected president and the will of the nation and refuse to participate in any action with the authority that stole the power and dealt violently with peaceful demonstrators."
It added, "Mohamed Morsy, president of Egypt, stresses that the measures that were announced by the General Command of the Armed Forces represent a full-fledged military coup which is unacceptable by every free person."
It called on demonstrators to show restraint.
The moves against the organization came as an uncertain new political order began to take shape with the swearing in of an interim president as well as the constitution's suspension on Wednesday.
State-run Al-Ahram News reported that Egypt's stock market surged 7% in the first hours of trading Thursday to a near two-month high.
The coup divided the millions of people who had taken to the streets across Egypt in recent days to defend or criticize Morsy's government.
It also raised questions about what will happen to Morsy and his supporters, who insist he remains the country's legitimate leader; whether violence blamed for the deaths Wednesday of at least 32 people will spread; whether democracy has a chance in Egypt.
But the Tamarod movement that had sought Morsy's ouster was moving on. It said in a tweet that it had nominated Mohamed ElBaradei, an opposition leader, to become prime minister.
ElBaradei told CNN on Thursday that Morsy's ouster was not a coup but was instead a "correction of the uprising of 2011."
Another opposition figure, Egyptian Conference Party leader Amre Moussa, took a similar semantic stance. "This is not a coup; this is a revolution," the former presidential candidate told CNN's Jim Clancy.
Asked whether the Brotherhood arrests were necessary, he said they would be temporary. "There are certain security measures that should not stay but for the first couple of days, three, four days -- the new regime wants to ensure that discipline will take place."
Democratic processes had been "absent" under Morsy, said the former Arab League secretary-general, who lost last year in his bid for the presidency.
Asked whether he would run again, he said, "I have declared several times before that I do not intend to run for president next time. This is my determination as I am talking to you."
The conflicting views, the threat of more violence, possible divisions among the anti-Morsy coalition and Egypt's economic woes represent major obstacles to a smooth transition, said Hani Sabra, director of the Middle Eastern arm of the Eurasia Group, a U.S.-based political risk research and consulting firm. "I don't think that the military's so-called road map is actually going to move smoothly. I think there are a lot of challenges it faces."
The huge crowds that had celebrated Morsy's ouster Wednesday night with horns, cheering, fireworks had thinned hours later. On Thursday, the atmosphere in Cairo's Tahrir Square was calm and celebratory. Crowds cheered as military helicopters flew overhead. Women pushed baby strollers, children had their faces painted, music played and people danced.
Morsy, a Western-educated Islamist elected a year ago, "did not achieve the goals of the people" and failed to meet the generals' demands that he share power with his opposition, Egypt's top military officer, Gen. Abdel-Fatah El-Sisi, said Wednesday in a televised speech to the nation.
Adly Mansour, head of the country's Supreme Constitutional Court, was sworn in Thursday as interim president in Cairo.
At the ceremony, Mansour said the Egyptian people had given him the authority "to amend and correct" the revolution that toppled Hosni Mubarak in 2011. Following a decree last month by Morsy, Mansour had become head of the court just two days earlier.
Until new elections, to be held at an unspecified date, Mansour will have the power to issue constitutional declarations, El-Sisi said.
The Egyptian military has dominated the country for six decades and took direct power for a year and a half after Mubarak's ouster.
Morsy's approval ratings plummeted after his election in June 2012 as his government failed to keep order or revive Egypt's economy.
Morsy's opponents accused him of authoritarianism and forcing through a conservative agenda, and on Monday the military gave him 48 hours to order reforms.
As the deadline neared Wednesday, he offered to form an interim coalition government to oversee parliamentary elections and revise the constitution, which was enacted in January. But those actions failed to satisfy the generals.
The army's move against Morsy and the Muslim Brotherhood, the long-repressed political movement that propelled him to office, provoked wildly conflicting reactions.
In Tahrir Square, the epicenter of two Egyptian upheavals, a vast gathering of Morsy's opponents erupted in jubilation and fireworks at El-Sisi's announcement Wednesday night.
"The crowd walked up to the barricades and started banging on them using rocks, sticks and even bare hands," said Sultan Zaki Al-Saud in a CNN iReport. "It sounded like thunder as the hollow barricades rang with every blow."
During his time in office, Morsy had squared off against Egypt's judiciary, the media, the police and even artists. Egyptians are frustrated with rampant crime and a struggling economy. Unemployment remains high, food prices are rising and there are frequently electricity cuts and long fuel lines.
Morsy had remained defiant.
"The world is looking at us today," he said Wednesday in a taped statement delivered to the Arabic satellite network Al Jazeera. "We by ourselves can bypass the obstacles. We, the sons of Egypt, the sons of this country -- this is the will of the people and cannot be canceled."
Shortly after Morsy's statement aired, Al Jazeera reported its Cairo studios had been raided during a live broadcast and 28 staff members arrested. Most were later released, it said.
On Thursday, Al Jazeera's acting chief, Mostefa Souag, demanded the immediate release of the Egyptian channel's managing director, Ayman Gaballah, and Al Jazeera Arabic broadcast engineer Ahmad Hasan.
"A return to Mubarak-era practices of mass arrests and politically motivated imprisonment of Muslim Brotherhood leaders will have the worst possible effect on Egypt's political future," said Human Rights Watch, the U.S.-based advocacy group.